Best Known (120−32, 120, s)-Nets in Base 16
(120−32, 120, 4096)-Net over F16 — Constructive and digital
Digital (88, 120, 4096)-net over F16, using
- net defined by OOA [i] based on linear OOA(16120, 4096, F16, 32, 32) (dual of [(4096, 32), 130952, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(16120, 65536, F16, 32) (dual of [65536, 65416, 33]-code), using
- 1 times truncation [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 168−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(16120, 65536, F16, 32) (dual of [65536, 65416, 33]-code), using
(120−32, 120, 47962)-Net over F16 — Digital
Digital (88, 120, 47962)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16120, 47962, F16, 32) (dual of [47962, 47842, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(16120, 65536, F16, 32) (dual of [65536, 65416, 33]-code), using
- 1 times truncation [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 168−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(16120, 65536, F16, 32) (dual of [65536, 65416, 33]-code), using
(120−32, 120, large)-Net in Base 16 — Upper bound on s
There is no (88, 120, large)-net in base 16, because
- 30 times m-reduction [i] would yield (88, 90, large)-net in base 16, but